1. Field of the Invention
The field of the present invention relates to active imaging systems that use multiple coherent beams for illuminating and imaging an object.
2. Background
Imaging of objects has been of interest to many civilian and military users for many years. Images can be obtained passively or actively. In general terms, passive imaging uses either naturally occurring electromagnetic rays (e.g., rays of the Sun or the Moon) that reflect or scatter from the object or electromagnetic radiation emanating from the object being imaged, or both. Active imaging, on the other hand, relies on an artificial illumination source which is often part of the imaging system.
One active imaging technique in the art is called Sheared Coherent Interferometric Photography (SCIP). This technique has been described at length in the following publications:    1. R. A. Hutchin. Sheared Coherent Interferometric Photography. A Technique for Lensless Imaging. SPIE Vol. 2029 Digital Image Recovery and Synthesis II (1993) pp. 161-168.    2. D. G. Voelz, J. D. Gonglewski, P. S. Idell. SCIP computer simulation and laboratory verification SPIE Vol. 2029 Digital Image Recovery and Synthesis II (1993) pp. 169-176.SCIP allows near-diffraction limited remote imaging of objects through turbulent media. SCIP utilizes three illuminating beamlets and a detector array comprised of discrete intensity detectors. The advantages of SCIP over conventional imaging techniques include the ability to image through phase aberrating media, for example, the atmosphere, and the potential for implementing large detector arrays that are necessary for long range high resolution imaging. One utility for such a system is imaging space objects (e.g., Earth orbiting satellites) from the ground. Another utility is imaging remote moving objects, such as targets from a moving platform, e.g., missile tracking.
SCIP operation makes use of the physical properties of speckle patterns. A speckle pattern is a random intensity pattern produced by the mutual interference of a set of wavefronts. Speckle patterns are created when a laser beam is scattered off a rough surface. Speckle patterns reflect off an object just like light off a mirror. Thus, if one moves the source 1 mm to the left, the speckle pattern scattered back from the target will move 1 mm to the right. Illuminating the object with three coherent beamlets at the same time results in three nearly identical interfering speckle patterns which can be observed or registered by a suitable sensor. Then by phase modulating the three beamlets with respect to each other, one can measure the phase differences between each of these speckle patterns. If one beamlet is considered the reference source, and another beamlet is shifted 1 mm in the x direction and the remaining beamlet is shifted 1 mm in the y direction, then the demodulated signals at the sensor will provide the discrete complex gradient of the speckle pattern at 1 mm spacing. These gradients can then be reconstructed in a noise-optimized manner to provide an excellent measurement of the full object speckle pattern at the detector plane. A simple Fourier transform will then produce the complex target image.
The algorithm or process used to reconstruct the full speckle field from the complex gradients is called a complex exponential reconstructor. The complex exponential reconstructor is used routinely in adaptive optic systems to provide accurate wavefront reconstructions.
In a typical SCIP system 100, schematically illustrated in FIG. 1, a laser transmitter 115 is configured to emit light at a predetermined wavelength in three beamlets 110 through three transmit apertures 118, and a detector array 130 is configured to receive light 125 scattered by an object 105 illuminated by the beamlets 110. The laser transmitter 115 may be coupled to a laser source 117. The detector array 130 is an array of individual intensity detectors 132. A processor 150 communicates with the detector array 130 and is configured to form images of the object 105 based upon the output from the detector array 160. The processor 150 may also be configured to control the laser transmitter 115. As shown in FIG. 1 detail, the three beamlets 110a, 110b, and 110c emanate from co-planar transmit apertures 118a, 118b, 118c located on the laser transmitter plane 116. A first reference beamlet 110a, a second beamlet 110b sheared in the x direction with respect to the referenced beamlet and a third beamlet 110c sheared in the y direction with respect to the reference beamlet form an “L” spatial pattern. The beamlets 110a, 110b, and 110c are also shifted slightly in frequency with respect to one another. The first reference beamlet 110a has frequency (ν0), the second x-sheared beamlet 110b has frequency (ν0+νx) and the third y-sheared beamlet 110c has frequency (ν0+νy). The frequency differences cause the beamlets to “beat” at the object at the difference frequencies. The beat frequencies are νx, νy, and νx−νy. The frequency shifts are usually very small compared to the actual frequencies of the beamlets. The frequency shifts may be realized using phase modulators included in the laser transmitter 115. The processor 150 may be configured to control the phase modulators associated with the beamlets. The beamlets 110 travel through a turbulent medium 120 and reach the object 105. The object 105 scatters the incident beamlets 110. The scattered laser light 125 produces a modulated speckled intensity pattern 135 at the detector array 130. Speckles are formed since the object surface usually has roughness on the order of the laser wavelength. The detector array 130 measures the spatial and temporal behavior of the modulated speckled intensity pattern 135.
The fields returned from the object can be written as follows:Ao(r,t)=√{square root over (I0)}a(r)exp(jφ(r))exp(j2πν0t)Ax(r,t)=√{square root over (Ix)}a(r+sx)exp(jφ(r+sx))exp(j2π(ν0+νx)t)Ay(r,t)=√{square root over (Iy)}a(r+sy)exp(jφ(r+sy))exp(j2π(ν0+νy)t)  Equation 1where I0, Ix, and Iy are the intensities of the reference, x, and y sheared beamlets (110a, 110b, and 110c), sx and sy are vectors representing the direction and magnitude of the x and y sheared beamlets 110b and 110c, and φ(r) is the phase of the reference beamlet (110a). The function a(r) represents a normalized (real valued) field amplitude so that the spatially averaged value of its intensity is 1.
The return light from these three beamlets are superimposed at the detector array and the resulting measured intensity pattern at point r and time t I(r,t) on the detector array is given by:I(r,t)=|Ao(r,t)+Ax(r+sx,t)+Ay(r+sy,t)|2  Equation 2
Equation 2 can be algebraically evaluated and re-written as follows:
                              I          ⁡                      (                          r              ,              t                        )                          =                              I            m                    ⁢                      {                          1              +                                                                    V                    x                                    ⁡                                      (                    r                    )                                                  ⁢                                  cos                  ⁡                                      [                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  v                          x                                                ⁢                        t                                            +                                              Δ                        ⁢                                                                                                  ⁢                                                                              ϕ                            x                                                    ⁡                                                      (                            r                            )                                                                                                                ]                                                              +                                                                    V                    y                                    ⁡                                      (                    r                    )                                                  ⁢                                  cos                  ⁡                                      [                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  v                          y                                                ⁢                        t                                            +                                              Δ                        ⁢                                                                                                  ⁢                                                                              ϕ                            y                                                    ⁡                                                      (                            r                            )                                                                                                                ]                                                              +                                                                    V                    xy                                    ⁡                                      (                    r                    )                                                  ⁢                                  cos                  ⁡                                      [                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  (                                                                                    v                              x                                                        -                                                          v                              y                                                                                )                                                ⁢                        t                                            +                                              Δ                        ⁢                                                                                                  ⁢                                                                              ϕ                            xy                                                    ⁡                                                      (                            r                            )                                                                                                                ]                                                                        }                                              Equation        ⁢                                  ⁢        3            where the mean intensity at a point r isIm=I0[a(r)]2+Ix[a(r+sx)]2+Iy[a(r+sy)]2 and the visibility factors areVx(r)=2Im−1√{square root over (I0Ix)}a(r)a(r+sx)Vy(r)=2Im−1√{square root over (I0Iy)}a(r)a(r+sy)Vxy(r)=2Im−1√{square root over (IxIy)}a(r+sx)a(r+sy)and the spatial phase differences are defined byΔφx(r)=φ(r)−φ(r+sx)Δφy(r)=φ(r)−φ(r+sy)Δφxy(r)=φ(r+sx)−φ(r+sy)
FIG. 2 illustrates the SCIP method 200. The process starts with step 210, namely illumination of the object 105. The processor 150 directs the laser transmitter 115 to send three pulsed or continuous beamlets 110 towards the object 105. During this illumination step 210 the processor 150 adjusts the phase modulators controlling the phases of the beamlets 110 in a way that produces slight shifts in the frequency of the outgoing beamlets 110. Next, at step 220, the detector array 130 receives and captures frames of modulated speckled intensity patterns 135. The measured speckled intensity pattern I(r,t) is a superposition of three patterns as defined above in Equation 2. The detector array measurements 160 are communicated to the processor 150. The measurements 160 which have been defined as I(r,t) can be demodulated at the beat frequencies νx, νy, and νx−νy to yield estimates of the intensity visibilities and phase differences also defined in Equation 3. The optical field amplitude of one of the beamlets (e.g., a(r)) can then be obtained from the visibility estimates. The optical phase of the wavefront (e.g., φ(r)) can be found using the phase difference estimates. Accordingly, at step 230, the processor 150 demodulates the measurements 160 to yield estimates of intensity visibilities and phase differences 232.
Several algorithms have been developed to recover the field amplitude and phase from the intensity measurements which are commonly collected and stored as a time series of samples. Three or four time samples per cycle of the highest beat frequency are typically considered adequate to determine the phase of the beat signal. Demodulation of beat frequencies can be done using a Fourier transform of the time series at each detector 132.
Once visibility and phase difference values are computed, the next step 240 is reconstructing the wavefront, that is, recovering the optical field amplitude and phase. The reconstructed wavefront is often an estimate of A0(r,t) as defined in Equation 1. At the following step 250, the reconstructed wavefront is inverse Fourier transformed and the squared modulus is computed to yield a two dimensional snapshot image 252. This two dimensional snapshot image 252 is often speckled. As explained earlier, this is due to the object surface having roughness on the order of the laser wavelength. A series of snapshot images 254 can be collected, registered, and averaged as shown in process 260 to reduce speckle noise in the final two dimensional image 262.
The SCIP system and method described above has two fundamental limitations. First, it can be used to make two dimensional images only. Since the two dimensional image generated by SCIP is a projection of the three dimensional object 105 onto a two dimensional image plane, the surface contours of the object 105 are not available. To obtain surface contours, one would need to compute the range to object 105 at multiple two dimensional image pixels. Second, even though it is virtually immune to turbulence effects near the detector array, SCIP is adversely impacted by turbulence, in particular anisoplanatic and scintillation effects.